I had two rats that had a head tilt problem. The first one went to the vet, got a steroid shot and some antibiotics. Got better, then all of a sudden one night she had it back again. Unfortunately, she passed not long after that. Her head tilt was sudden and not gradual though, so we believe she had some type of stroke. The other one I took in as a rescue until I was able to find her a home of her own. She had the head tilt for weeks before I took her and I had her for a month and she was fine when she went to her new home. Someone mentioned that it could be a sign of a vitamin deficiency. But it could also be a sign of an upper respiratory infection or ear infection.
What type of bedding do you use? Certain types of bedding aren't good for them and can lead to upper respiratory infections. (Cedar is one that is bad for all small animals. I believe I read that pine is also bad for degus, but I don't know for sure. Hopefully someone else can answer that one.) From what I heard, if you want to use a wood based bedding, aspen is best, so that's what I use. Stuff like carefresh and other recycled newspaper beddings are also good, but more expensive than aspen.